login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111203 x such that pi(x)/li(x) is greater than it is for all smaller x > 1.5. 0
2, 1051, 1063, 1069, 1097, 1103, 1109, 1123, 1129, 1303, 1307, 1321, 1327, 1619, 1621, 1627, 2399, 2447, 2477, 2719, 2731, 2753, 2801, 2803, 3929, 3931, 3947, 4273, 4289, 4297, 5851, 5857, 5861, 5867, 5869, 5881, 6367, 6373, 6379, 9433, 9437, 9439 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This will be a very long but finite sequence, since pi(x)/li(x) will exceed unity for some very large values of x (as Littlewood first showed) but then will asymptotically tend to unity by the prime number theorem. One large but unknown element of the sequence will be the smallest x for which pi(x)>li(x).

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

For 1.5<x<2, li(x)>0 and pi(x)=0, so pi(x)/li(x)=0. a(1)=2 because at x=2, pi(x)/li(x) has its increase, to 1/li(2)=0.9567878442. a(2)=1051 because x=1051 gives the next time pi(x)/li(x) gives a higher value, 177/Li(1051)=0.956932676.

MAPLE

with(numtheory): Digits:=50; s:=0: for n from 1 to 10000 do if (evalf(n/Li(ithprime(n)))>s) then s:=evalf(n/Li(ithprime(n))): print(ithprime(n)) else s:=s end if end do;

CROSSREFS

Sequence in context: A218437 A166852 A236951 * A159858 A108963 A152510

Adjacent sequences:  A111200 A111201 A111202 * A111204 A111205 A111206

KEYWORD

nonn,fini

AUTHOR

Don N. Page, Oct 24 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 4 23:59 EDT 2020. Contains 333238 sequences. (Running on oeis4.)